I just want to weigh in here since I have done a few re-wraps recently and have had many come through my hands as well. I am fairly certain from looking at the picture that this is the original wrap to the drum for 2 reasons.
1. I blew the pictures way up and looked at the photo of the bottom of the drum so I could see the grommet on the vent hole. There is no visible nicks or scaring on the inside of the shell that usually come with trying to remove the old grommets to get the badge of. Is it possible someone removed it and then sanded the inside of the shell to remedy that? Yes, but in my experience that is generally not the case. The inside of the shell has coloration to it that I would not associate with an interior that has been refinished.
2. Also looking at the closeups of the of the seem of the wrap, the seems sits right at the edge of the lug and I have seen that a lot on some older kits and I have also seen many kits where the seem sits in the middle of the lug. Putting the seam where it is in the photo just makes sense so that the lug will sit flat on the wrap. The wrap is also very thin, I have seen many different color wrap samples that have come my way recently and the modern wraps being offered by all of the online supply houses are much thicker than the wraps that were used years ago. The seem on this drum looks much too thin to be a modern re-wrap and if it were a re-wrap with current wraps then that seem would be noticeably thicker.
Just my :2Cents:, hope it helps. I will let everyone else debate proper tension rods and hoops etc.